Weingarten Calculus and the IntHaar Package for Integrals over Compact Matrix Groups
Abstract
In this paper, we present a uniform formula for the integration of polynomials over the unitary, orthogonal, and symplectic groups using Weingarten calculus. From this description, we further simplify the integration formulas and give several optimizations for various cases. We implemented the optimized Weingarten calculus in Maple in a package called IntHaar for all three compact groups. Here we will discuss its functions, provide instructions for the package, and produce some examples of computed integrals.
 Publication:

arXiv eprints
 Pub Date:
 December 2016
 arXiv:
 arXiv:1612.07641
 Bibcode:
 2016arXiv161207641G
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory
 EPrint:
 21 pages, 4 figures, software available at: http://www.math.rutgers.edu/~ag930/